Hello Gaz. Yup this certainly looks like a false widow and with its ruddy brown abdomen and light markings showing well in your photograph I would say that this is Steatoda noblis. I believe that they have been established in the Gosport, Portsmouth area for many years. I think that there can also be a darker version of this spider that appears almost black with a cream band around the edge of the abdomen. Don't worry about them though, despite their tabloid reputation they tend to be quite peaceable and retiring and only likely to give a nip if very threatened.